In Fig. 5.10, if AC = BD, then prove that AB = CD

Solution:

*

It is given, AC = BD

From the given figure, we get,

AC = AB+BC

BD = BC+CD

⇒ AB+BC = BC+CD [AC = BD, given]

We know that, according to Euclid’s axiom, when equals are subtracted from equals, remainders are also equal.

Subtracting BC from the L.H.S and R.H.S of the equation AB+BC = BC+CD, we get,

AB+BC-BC = BC+CD-BC

AB = CD

Hence Proved.